Meanings
Fig.: to be skeptic

Examples
“Don't you believe me? Are you saying that I'm a liar?” “Call me a doubting Thomas but I need to hear what happened from someone else too”
“E così non mi credi! Mi stai forse dando del bugiardo?” “Sarò come S. Tommaso, ma ho bisogno di sentire cosa è successo anche da qualcun altro”

I was a doubting Thomas, until I saw the results of pranotherapy with my own eyes
Nei confronti della pranoterapia ero un S. Tommaso: non ci ho creduto finché non ho visto i risultati con i miei occhi

I'm from Missouri: I need to be shown to believe
Sono come S. Tommaso: non ci credo finché non tocco con mano

Origin
The original doubting Thomas was the apostle Thomas, who refused to believe that Christ had risen from the dead after His crucifixion, until he saw Him from himself and touched Him